For example, if I and my friend are having a ride at 1000 mph and I shout towards him (speed of sound 700 mph). What would happen? Will the speed of the sound relative to the ground be 1700 mph? Or will it be something else? Why?

I agree. You haven't explained the setting properly. If you both are riding horses at 1000mph, and you shout to him, the effect heard will be different than if you both were in a closed car moving at 1000mph.
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mikhailcaziJul 11 '13 at 5:51

1 Answer
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The speed of sound is a property of the medium(air). So speed of sound is fixed with respect to the medium. As the medium is at rest with respect to the ground(assuming no wind), the speed of sound w.r.t ground will stay 700 mph.

If there is wind, you vectorialy add velocity of the wind and velocity of sound relative to air to get the velocity of sound w.r.t ground.